are the expressions 8x^2 + 3(x^2 + y) and 7x^2 + 7y + 4x^2 - 4y equivalent?
Yes.
8 x ^ 2 + 3 ( x ^ 2 + y ) =
8 x ^ 2 + 3 * x ^ 2 + 3 * y =
8 x ^ 2 + 3 x ^ 2 + 3 y =
11 x ^ 2 + 3 y
7 x ^ 2 + 7 y + 4 x ^ 2 - 4 y =
7 x ^ 2 + 4 x ^ 2 + 7 y - 4 y =
11 x ^ 2 + 3 y
thank you!
To determine if the expressions 8x^2 + 3(x^2 + y) and 7x^2 + 7y + 4x^2 - 4y are equivalent, we need to simplify both expressions and compare the results.
Let's start with the first expression: 8x^2 + 3(x^2 + y)
Step 1: Distribute the 3 to both terms inside the parentheses:
8x^2 + 3x^2 + 3y
Step 2: Combine like terms:
(8 + 3)x^2 + 3y
11x^2 + 3y
Now, let's simplify the second expression: 7x^2 + 7y + 4x^2 - 4y
Step 1: Combine like terms:
(7 + 4)x^2 + (7 - 4)y
11x^2 + 3y
After simplifying both expressions, we can see that they are indeed equivalent:
8x^2 + 3(x^2 + y) = 11x^2 + 3y = 7x^2 + 7y + 4x^2 - 4y
Therefore, the expressions 8x^2 + 3(x^2 + y) and 7x^2 + 7y + 4x^2 - 4y are equivalent.
To determine if the expressions 8x^2 + 3(x^2 + y) and 7x^2 + 7y + 4x^2 - 4y are equivalent, we need to simplify and compare them.
Let's start with the expression 8x^2 + 3(x^2 + y).
First, we can simplify the part inside the parentheses by distributing the 3 to both x^2 and y:
8x^2 + 3 * x^2 + 3 * y
This simplifies to:
8x^2 + 3x^2 + 3y
Next, we can combine like terms:
(8x^2 + 3x^2) + 3y
This gives us:
11x^2 + 3y
Now let's simplify the other expression, 7x^2 + 7y + 4x^2 - 4y.
Again, we can combine like terms:
(7x^2 + 4x^2) + (7y - 4y)
Simplifying further:
11x^2 + 3y
From the simplifications, we can see that both expressions result in 11x^2 + 3y. Therefore, the two expressions are equivalent.